Another omitted effect is the interference in the GW emission. In Eqs. (REF ), only the GW emitted by every single mode is included. The GW can also be produced by the transition from one mode to another, or by the annihilation of two scalars in different modes. The former can be calculated via the quadrupole formula and is negligible [1]}. The latter process has also been studied for modes with different \(l\) , such as \(\lbrace 0,1,1\rbrace \)  and \(\lbrace 0,2,2\rbrace \)  modes. From the scaling of the expressions in Eqs. (REF ), this interference is suppressed by \((M\mu )^2\)  compared to \(\dot{E}_\text{GW}^{(011)}\)  and is not important. To the contrary, the interference of the \(\lbrace 0,1,1\rbrace \)  and \(\lbrace 1,1,1\rbrace \)  modes is not suppressed. The signal is the strongest between \(t_1\)  and \(t_2\)  in Fig. REF , causing a beat feature of the GW waveform, which is the topic of the next section.
